Subgroups — C₂×C₃×C₁₆×C₃₀₇ #72206365

Order 29472.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₃₀₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₆×C₃₀₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₄×C₃₀₇	C₄	1	1	yes	characteristic
4	C₃×C₈×C₃₀₇	C₄	1	1	yes	characteristic
5	C₃×C₈×C₃₀₇	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₃₀₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₈×C₃₀₇	C₂×C₃	1	1	yes	characteristic
8	C₁₆×C₃₀₇	C₂×C₃	1	2	yes	direct product factor
9	C₂²×C₃×C₃₀₇	C₈	1	1	yes	characteristic
10	C₃×C₄×C₃₀₇	C₈	1	1	yes	characteristic
11	C₃×C₄×C₃₀₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₃₀₇	C₃×C₄	1	1	yes	characteristic
13	C₈×C₃₀₇	C₃×C₄	1	1	yes	characteristic
14	C₈×C₃₀₇	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×C₃₀₇	C₁₆	1	2	yes	direct product factor
16	C₂×C₃×C₃₀₇	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₃₀₇	C₃×C₈	1	1	yes	characteristic
18	C₄×C₃₀₇	C₃×C₈	1	1	yes	characteristic
19	C₄×C₃₀₇	C₂×C₃×C₄	1	1	yes	characteristic
20	C₃×C₃₀₇	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃₀₇	C₃×C₁₆	1	2	yes	direct product factor
22	C₂×C₃₀₇	C₂×C₃×C₈	1	1	yes	characteristic
23	C₃₀₇	C₂×C₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃×C₁₆	C₃₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×C₈	C₂×C₃₀₇	1	1	yes	characteristic
26	C₃×C₁₆	C₂×C₃₀₇	1	2	yes	direct product factor
27	C₂×C₁₆	C₃×C₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃×C₄	C₄×C₃₀₇	1	1	yes	characteristic
29	C₃×C₈	C₄×C₃₀₇	1	1	yes	characteristic
30	C₃×C₈	C₂²×C₃₀₇	1	1	yes	characteristic
31	C₂×C₈	C₂×C₃×C₃₀₇	1	1	yes	characteristic
32	C₁₆	C₂×C₃×C₃₀₇	1	2	yes	direct product factor
33	C₂²×C₃	C₈×C₃₀₇	1	1	yes	characteristic
34	C₃×C₄	C₈×C₃₀₇	1	1	yes	characteristic
35	C₃×C₄	C₂×C₄×C₃₀₇	1	1	yes	characteristic
36	C₂×C₄	C₃×C₄×C₃₀₇	1	1	yes	characteristic
37	C₈	C₃×C₄×C₃₀₇	1	1	yes	characteristic
38	C₈	C₂²×C₃×C₃₀₇	1	1	yes	characteristic
39	C₂×C₃	C₁₆×C₃₀₇	1	2	yes	direct product factor
40	C₂×C₃	C₂×C₈×C₃₀₇	1	1	yes	characteristic
41	C₂²	C₃×C₈×C₃₀₇	1	1	yes	characteristic
42	C₄	C₃×C₈×C₃₀₇	1	1	yes	characteristic
43	C₄	C₂×C₃×C₄×C₃₀₇	1	1	yes	characteristic
44	C₃	C₂×C₁₆×C₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×C₁₆×C₃₀₇	1	2	yes	direct product factor
46	C₂	C₂×C₃×C₈×C₃₀₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₃×C₃₀₇
socle, prime radical	C₂²×C₃×C₃₀₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃×C₁₆×C₃₀₇	C₂	direct (N × H)
6. C₂×C₁₆×C₃₀₇	C₃	direct (N × H)
8. C₁₆×C₃₀₇	C₂×C₃	direct (N × H)
15. C₂×C₃×C₃₀₇	C₁₆	direct (N × H)
20. C₃×C₃₀₇	C₂×C₁₆	direct (N × H)
21. C₂×C₃₀₇	C₃×C₁₆	direct (N × H)
23. C₃₀₇	C₂×C₃×C₁₆	direct (N × H)
24. C₂×C₃×C₁₆	C₃₀₇	direct (N × H)
26. C₃×C₁₆	C₂×C₃₀₇	direct (N × H)
27. C₂×C₁₆	C₃×C₃₀₇	direct (N × H)
32. C₁₆	C₂×C₃×C₃₀₇	direct (N × H)
39. C₂×C₃	C₁₆×C₃₀₇	direct (N × H)
44. C₃	C₂×C₁₆×C₃₀₇	direct (N × H)
45. C₂	C₃×C₁₆×C₃₀₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₈×C₃₀₇	2
C₃×C₁₆×C₃₀₇	2
C₂×C₁₆×C₃₀₇	3
C₂×C₃×C₁₆	307

Subgroups — C2×C3×C16×C307 #72206365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₆×C₃₀₇ #72206365